Prompting serves as the major way humans interact with Large Language Models (LLM). Commercial AI systems commonly define the role of the LLM in system prompts. For example, ChatGPT uses ``You are a helpful assistant'' as part of its default system prompt. Despite current practices of adding personas to system prompts, it remains unclear how different personas affect a model's performance on objective tasks. In this study, we present a systematic evaluation of personas in system prompts. We curate a list of 162 roles covering 6 types of interpersonal relationships and 8 domains of expertise. Through extensive analysis of 4 popular families of LLMs and 2,410 factual questions, we demonstrate that adding personas in system prompts does not improve model performance across a range of questions compared to the control setting where no persona is added. Nevertheless, further analysis suggests that the gender, type, and domain of the persona can all influence the resulting prediction accuracies. We further experimented with a list of persona search strategies and found that, while aggregating results from the best persona for each question significantly improves prediction accuracy, automatically identifying the best persona is challenging, with predictions often performing no better than random selection. Overall, our findings suggest that while adding a persona may lead to performance gains in certain settings, the effect of each persona can be largely random. Code and data are available at https://github.com/Jiaxin-Pei/Prompting-with-Social-Roles.